In this paper, we propose a multivariate Hawkes framework for modelling and predicting cyber attacks frequency. The inference is based on a public data set containing features of data breaches targeting the US industry. As a main output of this paper, we demonstrate the ability of Hawkes models to capture self-excitation and interactions of data breaches depending on their type and targets. In this setting, we detail prediction results providing the full joint distribution of future cyber attacks times of occurrence. In addition, we show that a non-instantaneous excitation in the multivariate Hawkes model, which is not the classical framework of the exponential kernel, better fits with our data. In an insurance framework, this study allows to determine quantiles for number of attacks, useful for an internal model, as well as the frequency component for a data breach guarantee.

中文翻译：

---

网络保险的多变量霍克斯流程

在本文中，我们提出了一个用于建模和预测网络攻击频率的多变量 Hawkes 框架。该推论基于一个公共数据集，其中包含针对美国行业的数据泄露特征。作为本文的主要输出，我们展示了 Hawkes 模型根据类型和目标捕获数据泄露的自激和交互的能力。在这种情况下，我们详细介绍了预测结果，提供了未来网络攻击发生时间的完整联合分布。此外，我们展示了多元霍克斯模型中的非瞬时激发，它不是指数核的经典框架，更适合我们的数据。在保险框架中，这项研究允许确定攻击次数的分位数，这对内部模型很有用，